IDS - Use Equations from Linear Models to Solve Problems Lesson

Scatter Plots and Predictions

Now, let's interpret our data!

image of scatter plot on graph; relationship between points scored and number of practices

The equation of the line of best fit in the above graph is y = 2x + 4. Use the graph and equation to answer the following questions. 

  1. What does the slope represent? What does the y-intercept represent?
    • Solution: Remember, that slope is defined as the change of y over the change in x. here that would be y (points scored) per x (number of practices), which is 2. The 
      • The y-intercept is the value of y when x is equal to zero. Therefore, the intercept should be the initial number of practices.
  2. Based on the line of best fit, find the number of points scored when the team has had 5 practices.
    • Solution: When x-5, y=14; Therefore, the number of points scored when there have been 5, practices is 14.
  3. Use the line of best fit to predict the points scored when the team has had 9 practices.
    • Solution: Substitute x=9 into the line of best fit equation and solve for y.
    • LaTeX: y=2x+4\\ y=2(9)+4\\ y=18+4\\ y=22y=2x+4y=2(9)+4y=18+4y=22
    • Therefore, the team will score 22 points in 9 practices.
  4. Write a statement that describes the relationship between the number of practices and the points scored.
    • Solution: As the number of practices increases, the number of points scored increases.

Use these steps to find a line of best fit equation for the data on a scatter plot.

  1. Draw the line of best fit for your data. Make sure you extend the line so that it crosses the y axis.
  2. Pick any two points on your line, and remember, these do not have to be points in your scatterplot.
  3. Use the slope formula to find the slope for your line.
  4. Locate the point on your line where the x coordinate is 0, or where the line crosses the y axis.
  5. Now, write your equation in slope-intercept form: y = mx + b  (m/slope and b/y intercept)
  6. Once you have written your equation, you can make predictions for any value of x or y just by plugging in your information.

Try It

Graph of baskets made

Y = mx + b

  m = ___________

  b =  ___________

Equation for Line of Best Fit _______________________

Number of Baskets at 22 Feet _____________________

Table of final exam scores

Y = mx + b

  m = ___________

  b =  ___________

Equation for Line of Best Fit _______________________

Score after 0 study hours      _______________________

Click here to check your answers. Links to an external site.

Practice

If you would like to practice more problems and check your work, click here. Links to an external site.  Make sure you check your answers and look at the course resources or ask your teacher if there are any problems you do not understand. Links to an external site.

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